The topology of the Brownian Bubbles, the supersets of the Brownian sheets, is notoriously hard to study: these supersets have fractal boundaries, and they typically form an archipelago of a countable family of ever smaller islands.
Yet a natural denoising tool, - persistent homology, - allows one to extract information about the largest topological patterns of Brownian Bubbles using some results about trees of Brownian walks, and an additive structure on them.